Introduction There are a number of manual and automated methods for determining volume and density. This article, however, focuses on laboratory methods that are most often used in research and quality control applications.
Another large area of application is on-line monitoring in production control. An excellent overview of density determinations in this application is by Capano (1).
The Density Enigma
When first introduced to density, perhaps in grade school, we were taught that it simply is the mass of an object divided by its volume. We thought that was pretty much the whole story, but sooner or later we discovered that this definition was only the beginning. The difficulty in defining density is exemplified by the American Society for Testing and Materials' book of standard definitions (1) where one finds over forty definitions based on mass per unit volume. The British Standards Institute (2) has narrowed it down to fourteen types of densities.
Determining the mass of an object is rather straightforward; it is the determination of volume that conceals the difficulty. The ‘volume' of a solid object, whether a single piece or a mass of finely divided powder, is one of those concepts that can't be bundled up into a single, neat definition.
A layman's dictionary typically defines volume in vague terms such as ‘the space occupied by an object.' McGraw-Hill's Dictionary of Scientific and Technical Terms (4) expands only slightly on that definition, offering "A measure of the size of a body or definite region in threedimensional space…." One must consult a particle technology's lexicon to appreciate the various conditions under which volume is defined. Two sources for these definitions are the British Standards Institute (BSI) and the American Society for Testing and Materials (ASTM). Here one finds that the ‘volume' of a material is the summation of several rigorously defined elemental volumes.
A common masonry brick will serve as a good example of an object that contains all types of elemental volumes and differs in material volume according to the measurement technique, measurement method, and conditions under which the measurements are performed. A brick obviously is composed of solid material and it has a volume that can be calculated after measuring its length, width, and thickness. However, it also contains surface irregularities, small fractures, fissures, and pores that both communicate with the surface and that are isolated within the structure. Voids that connect to the surface are referred to as open pores; interior voids inaccessible from the surface are called closed or blind pores.
Surface irregularities compose another type of void volume. For example, assume the bulk volume of the brick is determined from linear measurements of its length, width, and thickness. It generally is understood that the value of volume determined in this way is limited in accuracy because the surfaces are not perfect. If a perfect plane were to be laid on one of the surfaces, there would be many voids sandwiched between the two surfaces. For lack of a standard definition, this will be referred to as ‘external void volume' and will refer to the void volume between solid surface and that of a closely fitting envelope surrounding the object. It does not include pores that penetrate the interior of the particle. The meaning of the term is admittedly vague, but this volume can be determined or, at least, estimated under certain analytical conditions and can provide an indication of surface roughness. Figure 1 demonstrates the concept.
When a solid material is in granular or powdered form, the bulk contains another type of void: interparticle space. The total volume of interparticle voids depends on the size and shape of the individual particles and how well the particles are packed.